Unicellularity of the multiplication operator on Banach spaces of formal power series
Volume 147 / 2001
Studia Mathematica 147 (2001), 201-209
MSC: Primary 47B37; Secondary 47A25.
DOI: 10.4064/sm147-3-1
Abstract
Let $\{\beta(n)\}^{\infty}_{n=0}$ be a sequence of positive numbers and $1 \leq p < \infty$. We consider the space $\ell^{p}(\beta)$ of all power series $f(z)\hskip-2pt =\hskip-2pt \sum^{\infty}_{n=0} \skew4\widehat{f}(n)z^{n}$ such that $\sum_{n=0}^{\infty} |\skew4\widehat{f}(n)|^{p}|\beta(n)|^{p} < \infty$. We give some sufficient conditions for the multiplication operator, $M_{z}$, to be unicellular on the Banach space $\ell^{p}(\beta)$. This generalizes the main results obtained by Lu Fang [1].
